Abstract
Higher approximations of ray asymptotics are investigated by the boundary-layer method. For sources that are naturally called a center of pressure and a center of rotation, direction diagrams are found for transverse and longitudinal waves, respectively, which are absent in a homogeneous medium.
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A. P. Kiselev, “On the initial data for ray formulas describing high-frequency point sources in inhomogeneous elastic media,” Vopr. Din. Teor. Raspr. Seism. V.,XV, 6–27 (1975).
V. M. Babich and N. Ya. Kirpichnikova, The Method of the Boundary Layer in Diffraction Problems [in Russian], Leningrad (1974).
J. S. S. Avila and J. B. Keller, “The high-frequency asymptotic field of a point source in an inhomogeneous medium,” Commun. Pure Appl. Math.,26, No. 4, 363–382 (1961).
V. S. Vladimirov, Equations of Mathematical Physics, Marcel Dekker (1971).
G. E. Shilov, Mathematical Analysis, MIT Press (1974).
A. S. Alekseev, V. M. Babich, et al., “The ray method of computing the intensity of ray fronts,” Vopr. Dinam. Teor. Raspr. Seism. V.,5, No. 5, 3–24 (1961).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 99, pp. 28–42, 1980.
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Kiselev, A.P. High-frequency point sources in an inhomogeneous elastic medium. J Math Sci 20, 2407–2418 (1982). https://doi.org/10.1007/BF01087287
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DOI: https://doi.org/10.1007/BF01087287